A319983 -id:A319983 - cp's OEIS frontend

A317987 Discriminants of orders of imaginary quadratic fields with 2 classes per genus, negated.

39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 224, 252, 256, 259, 260, 264, 275, 276, 291, 292, 308, 320, 323, 328, 336, 355, 360, 363, 384, 387, 388, 400, 456, 468, 475, 504, 507, 528, 544, 552, 564, 568, 576, 580, 592, 600, 603, 612, 616, 624, 640

Offset: 1

Jianing Song, Oct 02 2018

k is a term iff the form class group of positive binary quadratic forms with discriminant -k is isomorphic to (C_2)^r X C_4.
This is a subsequence of A133676, so it's finite. It seems that this sequence has 324 terms, the largest being 87360.
The smallest number in A133676 but not here is 3600.

Jianing Song, Table of n, a(n) for n = 1..324
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.

Cf. A003171, A133676.

Fundamental terms are listed in A319983.

isA317987(n) = (-n)%4 < 2 && 2^(1+#quadclassunit(-n)[2])==quadclassunit(-n)[1]

The form class groups of positive binary quadratic forms with discriminant -39, -55, -56, -63, -68, -80 and -128 are all isomorphic to C_4, so 39, 55, 56, 63, 68, 80 and 128 are all members of this sequence.

cp's OEIS Frontend

A317987 Discriminants of orders of imaginary quadratic fields with 2 classes per genus, negated.

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